We develop $M$-estimation and deconvolution methodology with the goal of making well-founded statistical inference on an individual's blood alcohol level based on noisy measurements of their skin alcohol content. We first apply our results to a nonlinear least squares estimator of the key parameter that specifies the blood/skin alcohol relation in a diffusion model, and establish its existence, consistency, and asymptotic normality. To make inference on the unknown underlying blood alchohol curve, we develop a basis space deconvolution approach with regulazation, and determine the asymptotic distribution of the error process, thus allowing us to compute uniform confidence bands on the curve. Simulation studies show agreement between the performance of our curve estimators and their asymptotic distributions at low noise levels, and we apply our methods to a real skin alcohol data set collected via a transdermal biosensor.

翻译：我们发展了$M$-估计与反卷积方法论，旨在基于个体皮肤酒精含量的噪声测量，对其血液酒精水平进行可靠的统计推断。首先，将所得结果应用于扩散模型中刻画血液/皮肤酒精关系的关键参数的非线性最小二乘估计，并建立其存在性、相合性及渐近正态性。为对未知的潜在血醇曲线进行推断，我们提出了一种带正则化的基空间反卷积方法，确定了误差过程的渐近分布，从而可计算曲线的一致置信带。模拟研究表明，在低噪声水平下，曲线估计量的性能与渐近分布吻合良好，并将该方法应用于通过透皮生物传感器采集的真实皮肤酒精数据集。